I see that torsion must be checked in the boundary stability of the
lintel angle, but for the design of the angle, hopefully the vertical
leg will not have much differential rotation. And the differential
rotation is what will induce the torsional shear stresses. I can see
there being bending in the vertical leg from it resisting torsion, the
same type of bending induced in the horizontal leg from transferring
the weight of the block to the vertical leg.
Maybe there is a small amount of rotation difference of the angle
between anchor locations. But I don't think you have to design for the
full torsion, only that which overcomes the normal friction between
the block and the horizontal leg.
How many loose brick lintel angles have you ever seen? If torsion was
such a large factor, wouldn't the angles twist right out? I'm not
saying disregard it as a stability check, but I'm not sure if it is a
big design issue. I wouldn't know where to start designing an angle
for torsion either.
The problem is that the center of the application of force of brick is
2" off the face of the leg of a typical 3.5" angle, so take your
vertical force x 2" to get your torsion. Now, will this really happen?
Probably not - the brick is more likely to sag a bit, and the
application of force would shift back towards the leg, but that' would
be a non-conservative assumption. Since the shear center of an angle
runs through the center of the vertical leg, and angles have such low
polar moments, you can see "real" torsion. Now, the ends are generally
fixed by the weight of the brick above, which is a mitigating factor, as
is the L/600 deflection criteria that is used for design. Stress rarely
controls a brick angle design. I do know of cases where torsion was not
taken into account for a beam with a bottom flange extension plate
intended to support a brick facade - it rotated very badly.
It could be worse, it could be a channel - their shear centers are
behind the web, so you can't physically load a channel by itself through
its shear center and you always end up with some torsional component.
And, yes, torsion is a pain. Most texts spend all their effort on the
determinate form on solution, which is typically a fixed-free round bar,
with the advanced sections looking at non-circular sections. Rarely do
they discuss warping in any useful way, and usually there is little or
no discussion of a distributed force (most are point applications of
loads, as for transmission shafts or eccentric linkages). The discrete
forms of equations get ugly quickly - take a look at Tables 21 and 22 in
Roark for examples - and they're just for point-torques, not
distributed. Even Roark doesn't have distributed torque equations for
thin walled sections. (Actually, I don't think it has it for circular
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